Detecting the neutrino mass via the cross-correlation between matter tracers and the ISWRS effect?
This work explores the potential to detect the nonlinear Integrated Sachs Wolfe effect, namely the Rees-Sciama effect (ISWRS), by cross-correlating current and future Cosmic Microwave Background (CMB) experiments -- Simons Observatory, CMB-S4, CMB-HD, and PICO -- with ongoing Large Scale Structure (LSS) surveys, such as Euclid and the Vera Rubin Observatory (LSST). We model the cross-correlation of the ISWRS effect with gravitational potential tracers like galaxy clustering, cosmic shear, and CMB-lensing potential, to forecast results from these experiments. Our analysis also accounts for the presence of massive neutrinos to assess the feasibility of identifying the $ν$$Λ$CDM model and constraining the neutrino mass sum, M$ν$. Our findings indicate that the CMB-lensing potential reconstructed by CMB-HD is expected to provide the most promising results, achieving $\gtrsim$ 5$σ$ detections even under conservative assumptions for detector noise and foregrounds, thereby allowing differentiation between $ν$$Λ$CDM models. Galaxy clustering can also yield significant detections, whereas cosmic shear can provide valuable results only if non-linearities are accurately modelled, beyond the capabilities of currently available analytical approaches. These latter LSS probes do not provide strong constraining power on M$ν$. While our findings suggest that future CMB experiments and LSS surveys will enable the detection of the ISWRS effect, they do not imply significant prospects for imposing new constraints on neutrino masses in the near future.